
The search space is of cardinality \(\vert S_{\text{M}}(G) \vert = O(n)\) 
since for every time point \(k\) , only the local interval \((s, e) = (k - G, k + G)\)  is considered;
we sometimes denote that \(k \in \mathcal {S}_{\text{M}}(G)\)  where there is no confusion.
[1]} propose two criteria for the simultaneous localisation of the change points,
whereby each estimator is obtained as
a local maximiser of \(\vert \mathcal {T}_{s, k, e}(X) \vert , \, k \in \mathcal {S}_{\text{M}}(G)\) ,
over a sufficiently large interval relative to \(G\) ,
at which the scaled MOSUM statistic exceeds a theoretically motivated threshold.
